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VOL. 87 | 2021 Tightness of the solutions to approximating equations of the stochastic quantization equation associated with the weighted exponential quantum field model on the two-dimensional torus
Masato Hoshino, Hiroshi Kawabi, Seiichiro Kusuoka

Editor(s) Yuzuru Inahama, Hirofumi Osada, Tomoyuki Shirai

Abstract

We consider stochastic quantization associated with the weighted exponential quantum field model on the two-dimensional torus via a method of singular stochastic partial differential equations and show the tightness of the solutions to approximating equations of the stochastic quantization equation. If the model is not weighted, then the drift term of the stochastic quantization equation, which includes a renormalization term, is nonpositive or nonnegative. However, in the weighted case, generally the drift term is neither nonpositive nor nonnegative. We modify the argument in the case without weights and discuss the weighted model.

Information

Published: 1 January 2021
First available in Project Euclid: 20 January 2022

Digital Object Identifier: 10.2969/aspm/08710341

Subjects:
Primary: 35Q40 , 35R60 , 60H15 , 81S20

Keywords: Høegh-Krohn model , quantum fields theory , Singular SPDE , Stochastic quantization

Rights: Copyright © 2021 Mathematical Society of Japan

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